Mathematics (Factoring and Logarithms)

This is a discussion on Mathematics (Factoring and Logarithms) within the A Brief History of Cprogramming.com forums, part of the Community Boards category; I have a question. My book does not cover this, and I have been unable to locate anything on this ...

Mathematics (Factoring and Logarithms)

I have a question. My book does not cover this, and I have been unable to locate anything on this online. Can you Factor inputs out of a logarithm?
Is the following valid? Please forgive the elementary question, but I feel it is important to get a good grasp on math to fine tune my code.

if this is valid, what other properties/laws can I apply to logarithms?
associative, distributive, etc.
is there a list of these?
I found this site, but no answer to these questions.http://mathworld.wolfram.com/Logarithm.html

Naturally I didn't feel inspired enough to read all the links for you, since I already slaved away for long hours under a blistering sun pressing the search button after typing four whole words! - Quzah

You. Fetch me my copy of the Wall Street Journal. You two, fight to the death - Stewie

I attended the tutorial session at my university, and the instructor in charge stated you can use the distributive law when dealing with logarithms. Is this not correct? If you can use distributive, wouldn't that allow the use of factoring out a common factor?

I found the name of the properties I was questioning.
Properties of Real Numbers.
I was advised by an instructor in a tutorial session, that you can use the Commutative, Associative, and Distributive properties on logarithms. Is this correct?
If you can use the Distributive property, couldn't you reverse that property?
This would be similar to factoring out a common multiple of the product.
Is this not a valid statement? Again, I just want to know if this is possible for future knowledge.

Naturally I didn't feel inspired enough to read all the links for you, since I already slaved away for long hours under a blistering sun pressing the search button after typing four whole words! - Quzah

You. Fetch me my copy of the Wall Street Journal. You two, fight to the death - Stewie

Your problem is that x is not in the domain of ln. That is why you come up with a non-sense result. Surely, the one solution of 2x=3x is x=0, but 0 is not in the domain of ln, so that equation ln(2x)=ln(3x) has no solution. The properties of logarithms only apply when the quantities in question are in the domain.

To convince yourself that 0 is not in the domain, look at the definition of ln(x). Integral{t=1 to t=x} of dt/t. If you just sketch it out, you see that this integral is undefined (i.e. the 'area under the curve' between 0 and 1 inclusive diverges sharply).

You don't need integrals to see the domain of ln x. ln x is just the inverse of e^x. e^x has a domain of (-inf, +inf) and a range of (0, +inf). Since e^x is a one to one type of function we don't have to restrict it to take the inverse. So its inverse will have a domain of (0, +inf) and a range of (-inf, +inf)

From IM
How would factoring with logarithms work?
If at all. Would I have to resolve the logarithm first before any attempt to factor?

You can not "factor" out of a log just as you can't "factor" out the base of an exponent. ie:

Code:

x^2 + x^3 != x ( 1^2 + 1^3)

I think you are forgetting the major rule: Once you get an answer put it into the orginal equation and check the results.